From a Geometrical Point of View explores historical and
philosophical aspects of category theory, trying therewith to
expose its significance in the mathematical landscape. The main
thesis is that Klein's Erlangen program in geometry is in fact a
particular instance of a general and broad phenomenon revealed by
category theory. The volume starts with Eilenberg and Mac Lane's
work in the early 1940's and follows the major developments of the
theory from this perspective. Particular attention is paid to the
philosophical elements involved in this development. The book ends
with a presentation of categorical logic, some of its results and
its significance in the foundations of mathematics.
From a Geometrical Point of View aims to provide its readers
with a conceptual perspective on category theory and categorical
logic, in order to gain insight into their role and nature in
contemporary mathematics. It should be of interest to
mathematicians, logicians, philosophers of mathematics and science
in general, historians of contemporary mathematics, physicists and
computer scientists.
General
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